抛物型SPDE中假设检验的中偏差原理精选.pdfVIP

Pure Mathematics 理论数学, 2015, 5, 28-33 Published Online March 2015 in Hans. /journal/pm /10.12677/pm.2015.52005 Moderate Deviations of Hypothesis Testing in Stochastic Partial Differential Equations Ruwei Cui Nanjing University of Aeronautics and Astronautics, Nanjing Jiangsu Email: cuiruwei@126.com th th nd Received: Feb. 12 , 2015; accepted: Feb. 25 , 2015; published: Mar. 2 , 2015 Copyright © 2015 by author and Hans Publishers Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). /licenses/by/4.0/ Abstract In this paper, we focus our attention on the hypothesis testing problem for the drift coefficient in the diagonalizable stochastic evolution equation driven by additive fractional Brownian motion 1   with Hurst parameter H ∈ ,1 . And when the dimension N is fixed and observation time T tends 2   to infinity, with the help of moderate deviations for the log-likelihood ratio process, we give the negative regions and obtain the decay rates of the error probabilities. Moreover, we also apply our results to some examples. Keywords Fractional Brownian Motion, Stochastic Partial Differential Equation, Hypothesis Testing, Moderate Deviation 抛物型SPDE中假设检验的中偏差原理 崔汝伟 南京航空航天大学，江苏 南京 Email: cuiruwei@126.com 收稿日期：2015年2月12 日；录用日期：2015年2月25 日；发布日期：2015年3月2 日 28 抛物型SPDE 中假设检验的中偏差原理 摘 要 本论文的目的是研究由可加分布朗运动驱动的随机偏微分方程中漂移系数的假设检验问题，其中Hurst 1